The invention relates to an apparatus and method for compensating IQ imbalance, and more particularly, to an apparatus and method for compensating IQ imbalance in an OFDM system when a carrier frequency offset exists.
In a normal communication system, in order to increase utilization efficiencies of the communication bandwidth, the communication bandwidth is often divided into several sub-channels and the orthogonal frequency division multiplexing (OFDM) technique is utilized to perform the signal transmissions and receptions. The above-mentioned communication system is called as OFDM communication system. For example, in the digital video broadcasting-terrestrial (DVB-T) standard, the radio signal received by the antennas of the receiver is a time-domain sequential signal composed of a plurality of OFDM symbols. In addition, the OFDM symbols can be transformed into an OFDM frequency-domain signal by a well-known Fourier transformation unit. As is known by those of average skill in the art, the OFDM frequency-domain signal is composed of a plurality of sub-carriers.
Please refer to FIG. 1, which is a diagram of an OFDM receiver 100. As shown in FIG. 1, the OFDM receiver 100 comprises an antenna 102, a low noise amplifier (LNA) 104, an in-phase mixer 106, a quadrature-phase mixer 108, a plurality of low-pass filters (LPF) 110 and 112, a plurality of analog-to-digital converters (ADC) 116 and 118, and a compensation module 114. First, the antenna 102 is utilized to receive a radio signal R1(t). The LNA 104 is utilized to amplify the radio signal R1(t) received by the antenna 102 to output a radio signal R2(t). And then, the in-phase mixer 106 is utilized to mix the radio signal R2(t) and an in-phase carrier 2 cos(2πfCt) to generate an in-phase analog signal RI(t). Next, the quadrature-phase mixer 108 is utilized to mix the radio signal R2(t) and a quadrature-phase carrier 2 sin(2πfCt) to generate a quadrature-phase analog signal RQ(t). Please note that the amplitude coefficient 2 of the in-phase carrier 2 cos(2πfCt) and the quadrature-phase analog signal 2 sin(2πfCt) is only utilized for simply illustrating the following equations. In other words, the amplitude parameter is possible to be any other values. This is not a limitation of the present invention. Next, the LPFs 110 and 112 are respectively utilized to filter out the high-frequency parts of the in-phase analog signal R1(t) and the quadrature-phase analog signal RQ(t) to output the filtered in-phase analog signal R′I(t) and filtered quadrature-phase analog signal R′Q(t). Finally, the ADCs 116 and 118 are respectively utilized to convert the in-phase analog signal R′1(t) and the quadrature-phase analog signal R′Q(t) into digital signals R′I[n] and R′Q[n]. The digital signals R′I[n] and R′Q[n] are inputted into the compensation module 114 to perform related signal processing.
As known by those skilled in the art, the above-mentioned in-phase carrier 2 cos(2πfCt) and the quadrature-phase carrier 2 sin(2πfCt) ideally correspond to a 90-degree phase difference such that the mixed in-phase analog signal RI and the mixed quadrature-phase analog signal RQ can be orthogonal. However, in the actual circuit, some factors such as, temperature, manufacturing procedure, and the supplying voltage shift, may cause a gain imbalance and a phase imbalance of the in-phase carrier 2 cos(2πfCt) and the quadrature-phase carrier 2 sin(2πfCt). This also causes a gain imbalance and a phase imbalance of the mixed in-phase analog signal RI and the mixed quadrature-phase analog signal RQ. In general, omitting the influences caused by the gain of the LNA 104 and related noises, the radio signal R2(t) input into the in-phase mixer 106 and the quadrature mixer 108 can be represented by the following equation as:R2(t)=Re{[rI(t)+jrQ(t)]ej2πfCt}  Equation (1)
In equation (1), rI(t) represents an in-phase analog signal transmitted by a transmitter (not shown), and rQ(t) represents a quadrature-phase analog signal transmitted by the transmitter. At this time, please consider the influences of a gain imbalance ε and a phase imbalance θ on the OFDM receiver 100 when the in-phase mixer 106 receives an in-phase carrier 2 cos(2πfCt) and the quadrature-phase mixer 108 receives the quadrature-phase mixer −2(1+ε)sin(2πfCt+θ). Therefore, the in-phase analog signal RI(t) and the quadrature-phase RQ(t) generated by the OFDM receiver 100 can be represented by the following equation as:
                                                                                          R                  I                                ⁡                                  (                  t                  )                                            =                            ⁢                              Re                ⁢                                                                  ⁢                                                      {                                                                  [                                                                                                            r                              I                                                        ⁡                                                          (                              t                              )                                                                                +                                                                                    jr                              Q                                                        ⁡                                                          (                              t                              )                                                                                                      ]                                            ⁢                                              ⅇ                                                  j2π                          ⁢                                                                                                          ⁢                                                      f                            c                                                    ⁢                          t                                                                                      }                                    ·                  2                                ⁢                cos                ⁢                                                                  ⁢                                  (                                      2                    ⁢                    π                    ⁢                                                                                  ⁢                                          f                      c                                        ⁢                    t                                    )                                                                                                        =                            ⁢                                                2                  ⁢                                                            r                      I                                        ⁡                                          (                      t                      )                                                        ⁢                                                                          ⁢                  cos                  ⁢                                                                          ⁢                                      (                                          2                      ⁢                      π                      ⁢                                                                                          ⁢                                              f                        c                                            ⁢                      t                                        )                                    ⁢                                                                          ⁢                  cos                  ⁢                                                                          ⁢                                      (                                          2                      ⁢                      π                      ⁢                                                                                          ⁢                                              f                        c                                            ⁢                      t                                        )                                                  -                                                                                                      ⁢                              2                ⁢                                                      r                                                                                                              ⁢                      Q                                                        ⁡                                      (                    t                    )                                                  ⁢                                                                  ⁢                sin                ⁢                                                                  ⁢                                  (                                      2                    ⁢                    π                    ⁢                                                                                  ⁢                                          f                                                                                                                        ⁢                        c                                                              ⁢                    t                                    )                                ⁢                                                                  ⁢                cos                ⁢                                                                  ⁢                                  (                                      2                    ⁢                    π                    ⁢                                                                                  ⁢                                          f                      c                                        ⁢                    t                                    )                                                                                                        =                            ⁢                                                                    r                    I                                    ⁡                                      (                    t                    )                                                  +                                                                            r                      I                                        ⁡                                          (                      t                      )                                                        ⁢                                                                          ⁢                  cos                  ⁢                                                                          ⁢                                      (                                          4                      ⁢                      π                      ⁢                                                                                          ⁢                                              f                        c                                            ⁢                      t                                        )                                                  -                                                                            r                      Q                                        ⁡                                          (                      t                      )                                                        ⁢                                                                          ⁢                  sin                  ⁢                                                                          ⁢                                      (                                          4                      ⁢                      π                      ⁢                                                                                          ⁢                                              f                        c                                            ⁢                      t                                        )                                                                                                          Equation        ⁢                                  ⁢                  (          2          )                                                                                                              R                                                                                                    ⁢                    Q                                                  ⁡                                  (                  t                  )                                            =                            ⁢                              Re                ⁢                                                                  ⁢                                                      {                                                                  (                                                                                                            r                              I                                                        ⁡                                                          (                              t                              )                                                                                +                                                                                    jr                              Q                                                        ⁡                                                          (                              t                              )                                                                                                      )                                            ⁢                                              ⅇ                                                  j2π                          ⁢                                                                                                          ⁢                                                      f                            c                                                    ⁢                          t                                                                                      }                                    ·                                                                                                                      ⁢                              (                                                      -                    2                                    ⁢                                                                          ⁢                                      (                                          1                      +                      ɛ                                        )                                    ⁢                                                                          ⁢                  sin                  ⁢                                                                          ⁢                                      (                                                                  2                        ⁢                        π                        ⁢                                                                                                  ⁢                                                  f                                                                                                                                            ⁢                            c                                                                          ⁢                        t                                            +                      θ                                        )                                                  )                                                                                        =                            ⁢                              2                ⁢                                                                  ⁢                                  (                                      1                    +                    ɛ                                    )                                ⁢                                  (                                                                                    -                                                  r                                                                                                                                            ⁢                            I                                                                                              ⁢                                              (                        t                        )                                            ⁢                                                                                          ⁢                      cos                      ⁢                                                                                          ⁢                                              (                                                  2                          ⁢                          π                          ⁢                                                                                                          ⁢                                                      f                                                                                                                                                      ⁢                              c                                                                                ⁢                          t                                                )                                            ⁢                                                                                          ⁢                      sin                      ⁢                                                                                          ⁢                                              (                                                                              2                            ⁢                            π                            ⁢                                                                                                                  ⁢                                                          f                                                                                                                                                                ⁢                                c                                                                                      ⁢                            t                                                    +                          θ                                                )                                                              +                                                                                                                                        ⁢                                                                    r                    Q                                    ⁡                                      (                    t                    )                                                  ⁢                                                                  ⁢                sin                ⁢                                                                  ⁢                                  (                                      2                    ⁢                    π                    ⁢                                                                                  ⁢                                          f                      c                                        ⁢                    t                                    )                                ⁢                                                                  ⁢                sin                ⁢                                                                  ⁢                                  (                                                            2                      ⁢                      π                      ⁢                                                                                          ⁢                                              f                        c                                            ⁢                      t                                        +                    θ                                    )                                            )                                                                          =                            ⁢                                                (                                      1                    +                    ɛ                                    )                                ⁢                                  (                                                                                    -                                                                              r                            I                                                    ⁡                                                      (                            t                            )                                                                                              ⁢                                                                                          ⁢                      sin                      ⁢                                                                                          ⁢                                              (                        θ                        )                                                              -                                                                                            r                          I                                                ⁡                                                  (                          t                          )                                                                    ⁢                                                                                          ⁢                      sin                      ⁢                                                                                          ⁢                                              (                                                                              4                            ⁢                            π                            ⁢                                                                                                                  ⁢                                                          f                              c                                                        ⁢                            t                                                    +                          θ                                                )                                                              +                                                                                                                                        ⁢                                                                                          r                      Q                                        ⁡                                          (                      t                      )                                                        ⁢                                                                          ⁢                  cos                  ⁢                                                                          ⁢                                      (                    θ                    )                                                  -                                                                            r                      Q                                        ⁡                                          (                      t                      )                                                        ⁢                                                                          ⁢                  cos                  ⁢                                                                          ⁢                                      (                                                                  4                        ⁢                        π                        ⁢                                                                                                  ⁢                                                  f                          c                                                ⁢                        t                                            +                      θ                                        )                                                              )                                                          Equation        ⁢                                  ⁢                  (          3          )                    
It can be determined utilizing the equations (2) and (3) that after the LPFs 110 and 112 filter out the high-frequency parts of the in-phase analog signal RI(t) and the quadrature-phase RQ(t), that the in-phase analog signal R′I(t) and the quadrature-phase analog signal R′Q(t) can be represented by the following equation as:R′I(t)=rI(t)  Equation (4)R′Q(t)=(1+ε)[rQ(t)cos θ−rI(t)sin θ]  Equation (5)
Furthermore, after being digitized by the ADCs 116 and 118, the in-phase digital signal R′I[n] and the quadrature-phase digital signal R′Q[n] can be represented by the following equations as:R′I[n]=rI[n]  Equation (6)R′Q[n]=(1+ε)[rQ[n] cos θ−rI[n] sin θ]  Equation (7)
In the related art, methods utilized in the OFDM receiver to compensating for the IQ imbalance comprise: (1) Utilize an adaptive frequency-domain equalizer (AFEQ). This reference can be found in the paper by A. Schuchert, R. Hasholzner, “A Novel IQ Imbalance Compensation Scheme for the Reception of OFDM Signals,” IEEE Trans. On Consumer Electronics, Vol. 43, No. 3, August 1998. (2) Utilize an adaptive time-domain compensator (ATDC). This can be referred to as a paper S. Fouladifard, H. Shafiee, “On Adaptive cancellation of IQ Mismatch in OFDM Receivers,” Proc. ICASSP 2003 IEEE International Conference on, Vol. 4, 6-10 April 2003 Pages: IV-564-7. (3) Utilize a decision feedback correction scheme (DFCS). This can be refer to as a paper J. Tubbax, B. Come, L. Van der Perre, L. Deneire, S. Donnay, M. Engels, “Compensation of IQ imbalance in OFDM systems,” Communications, 2003. ICC '03. IEEE International Conference on, Volume: 5, 11-15 May 2003 Pages: 3403-3407.
Because the above-mentioned mechanisms for compensating IQ imbalance are well-known by those skilled in the art, descriptions of the detailed circuit and operations are omitted here. However, the above-mentioned mechanisms for compensating IQ imbalance never mention the negative influences of the carrier frequency offset. In fact, the carrier frequency offset and the IQ imbalance both contribute to ruining the orthogonal properties of sub-carriers in the OFDM system. A main reason that the carrier frequency offset exists is the imbalance between the oscillator of the transmitter and the mixer of the receiver. A secondary cause of the carrier frequency offset is the Doppler shift generated because of the corresponding movements between the transmitter and the receiver.
While considering the carrier frequency offset and the IQ imbalance individually, the compensation of the carrier frequency offset and the IQ imbalance each requires its own method. However, while the two effects both exist, there is no one method to simultaneously solve the two problems. As a result, the compensation performance is degraded. The above-mentioned three IQ imbalance compensation mechanisms can be utilized to solve only the IQ imbalance, however, they cannot solve the carrier frequency offset imbalance. Therefore, if the characteristic of the circuit further comprises the carrier frequency offset, the above-mentioned three IQ imbalance compensation mechanisms are insufficient. Therefore, when the in-phase carrier of the in-phase mixer 106 and the quadrature-phase carrier of the quadrature-phase mixer 108 have the carrier frequency offset, according to related experiments, the OFDM 100 cannot compensate the gain imbalance ε and the phase imbalance θ by utilizing the above-mentioned three ways of compensation. In other words, if the carrier frequency offset exists, the efficiency of the above-mentioned three ways of compensation will be decreased enormously.